An adaptive finite‐time stable control law for manipulator robots with unknown parameters

This paper investigates the attitude tracking problem for spacecraft with limited communication, network congestion, unknown model parameters, actuator saturation, and external disturbances. To alleviate communication load, a novel sigmoid event-triggered mechanism is proposed with the special ability to guarantee a high minimum inter-execution time to avoid network congestion like package loss or time delay effectively. A neural network-based adaptive control algorithm is designed to deal with unknown model parameters. Besides, the problem of actuator saturation is tackled by introducing a dynamic loop gain function-based approach. System stability is proved by Lyapunov stability analysis and the high minimum inter-event time is substantiated by Zeno Behavior analysis with explanatory remarks. Numerical simulation results also show that a high minimum inter-event time and a high average inter-event time can be realized on the premise of high attitude tracking accuracy. Compared with all the previous studies, the ratio of the minimum inter-execution time to the average minimum inter-execution time has been improved by nearly 10 times with the proposed approach. Note to Practitioners—This paper was motivated by the problem of spacecraft attitude takeover control, but it also applies to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited communication for attitude takeover control of spacecraft by reducing the number of times wireless communication is required. This paper proposes a new method for realizing quasi-periodic control with a large time gap between any two consistent control impulses using a hyperbolic tangent function or another sigmoid function in an event-triggered mechanism. The proposed sigmoid event-triggered mechanism (ETM) can magnify the event-triggered threshold dozens of times in a short time to avoid unnecessary frequent triggering without decreasing the precision of control. It’s feasible to employ the proposed sigmoid ETM to deal with limited communication and network congestion in other network control systems that are constructed with similar dynamic structures. Furthermore, it would be marvelous if we could transform this sigmoid ETM into a high-efficiency decision-making mechanism in some control systems without using a wireless network. Now we are studying how to realize orbital-attitude (maneuver) control with a relatively average time interval and fewer times of orbit transfer by using the proposed sigmoid ETM. Besides, to further improve the system performance, we are also seeking to further increase the ratio of the minimum inter-execution time to the average inter-execution time. For the purpose of a more even distribution of the triggering events on the time axis, we may modify the proposed sigmoid event-triggered method or associate it with other methods.

Adaptive fuzzy asymptotic tracking control of uncertain nonaffine nonlinear systems with non-symmetric dead-zone nonlinearities

This article investigates the robust observer-based controller design problem for nonlinear parameter-varying systems subject to uncertainty and external disturbances. First, a novel augment vector is constructed, and an corresponding model of the resulting closed-loop system is obtained. Second, by applying the Lyapunov stability theory, a class of state-and-parameter-dependent robust asymptotic stability criteria is established, and the state-and-parameter-dependent sufficient conditions for the design of the robust observer-based controller are then acquired to guarantee the stability of the resulting closed-loop system, which can be effectively solved by sum-of-squares techniques. Different from the previous researches, the proposed control algorithm enables the state-and-parameter-dependent observer and the state-and-parameter-dependent controller design of the nonlinear parameter-varying systems to enjoy the advantage of separate design. The advantage can effectively reduce the computational complexity. Finally, simulation results demonstrate that the proposed robust observer-based controller shows improved performance in presence of uncertainty and external disturbances.

A formulation of the coupled modeling and robust control design problem is presented. The distinguishing feature is the treatment of the control design model as a degree of design freedom. A simple example highlights the potential improvement in closed-loop performance under the coupled approach. Quantification of the strength of the coupling in terms of performance boundaries is also described. >

This paper is concerned with the problem of robust controller design for electro-hydraulic servo systems driven by double-rod hydraulic actuators. Firstly, by introducing a linear varying parameter, an electro hydraulic servo system is described as a linear parameter varying(LPV) model. Secondly, based on this LPV model and a parameter-dependent Lyapunov approach, two parameter-dependent controllers are established for the stabilization and tracking problems, respectively. The obtained controllers are simple and their gains can vary with the parameter measured online. Finally, the numerical simulations demonstrate the satisfactory performance of the proposed controllers.

Robust control for nonlinear systems with structured [formula omitted]2-gain bounded uncertainty

This article focuses on establishing a general robust actor‐critic online learning control structure for disturbed nonlinear continuous systems with input constraints. It enriches the existing studies for the robustness of input constraint systems. First, the problem of robust controller design is successfully transformed into optimal controller design, and this process is proven, in which a particular nonquadratic discount cost function is defined. Then, build two neural networks (NNs) to estimate the cost function together and update each other. In the update process of actor NN, a robust term related to the state is introduced, which can guarantee the system's stability during the online learning process, and the state information is more fully utilized. Furthermore, using Lyapunov's direct method, it is proved that the estimated weights of the closed‐loop optimal control system and the actor‐critic NNs are uniformly ultimately bounded (UUB). It also provides extended discussions and a simulation example to demonstrate the robustness verification results of the novel algorithm.

This paper presents a Radial Basis Function neural network based higher-order Sliding Mode Control for robust control of a dynamical system. A conventional sliding mode controller is suffering from a chattering problem, and the Super Twisting Algorithm is a special kind of higher-order Sliding Mode Control that has the capability of minimizing the chattering problem. There are also unknown model parameters and external disturbances that exert a negative influence on the control performance. To address the issues of model uncertainties and chattering, a Radial Basis Function (RBF) neural network based Super Twisting Algorithm is designed. The RBF neural network evaluates the model parameters and uncertainties, while the Super Twisting approach mitigates chattering, hence improving the controller’s overall performance. Lyapunov stability based adaptive laws are derived for online updating of the parameters of the neural network. The proposed control algorithm was tested on a 2-degree-of-freedom serial flexible joint robotic arm to investigate its efficacy. The controller has a lower control chattering amplitude, lower control energy consumption, and a good tracking response, when compared to the RBF based conventional Sliding Mode controller and simple STA controller, as shown by the results.

The kinematics model and dynamics model of laser guided measuring robot (LGMR) are established based on the research on its structure and working principle. In deal with the moving deviation of LGMR caused by the characteristic inconsistent of two independent driving motors, a novel adaptive tracking control algorithm is proposed based on LGMR dynamic model. The control algorithm can compensation the uncertainties and interference of LGMR in real time. The unknown model parameters and disturbance are overcome effectively. Also, the stability of the control algorithm is proved with Lyapunov stability theory. Intensive experimental studies have been presented to confirm the effectiveness of the proposed algorithm; the results show that the control algorithm can be integrated to LGMR and guided it to required destination under automaticity and accuracy constraints, and prove efficiency and correctness of this control algorithm.

This paper addresses the problem of robust output feedback controller design with guaranteed cost and multiple quadratic Lyapunov function for linear switched systems in the continuous-time domain. The approach followed in this paper looks at the existence of switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality based conditions allow checking the existence of a family of quadratic Lyapunov functions. Then, a switched robust output feedback design method is established. The proposed method is illustrated on numerical example.

This paper proposes an algorithm of leader-following consensus control of multiple fixed-wing unmanned aerial vehicles’(UAVs) attitudes with time delays and unknown external disturbances. Firstly, a distributed controller based on undirected graph for leader-following consensus control of multi-UAVs’ attitudes is proposed. Then, the effects of time delays are compensated with the help of Lyapunov-Krasovskii function, Cauchy and Young’s inequality. Secondly, RBF neural network is introduced to estimate and reduce the negative effects of external disturbances. Finally, the effectiveness of the proposed distributed controller is demonstrated by Lyapunov theory and simulations.

Allowing for simultaneous occurrence of multiple actuator faults in signal channels, the problem of robust reliable tracking controller design for a class of uncertain systems with polytopic type uncertainty is investigated. Based an unstructured quadratic separator, a less conservative condition for the existence of a reliable tracking control is derived. In order to reduce the design conservatism, a parameter dependent formation is introduced in construction of the quadratic separator, which can give rise to the improvement in degree of freedom for controller synthesis. In addition, the condition mentioned above can be reduced to linear matrix inequalities (LMI). Finally an example is given to demonstrate the effectiveness and superiority of presented robust reliable tracking controller.

ROBUST NETWORKED OUTPUT FEEDBACK PREDICTIVE CONTROLLER DESIGN

This article deals with the problem of robust low-order controller design for systems with multimodel representations. Such models are frequently used for the description of nonlinear and complex industrial power systems over an operating profile. We first develop a generalized complex extension of convex direction based on the interpolation and edge theorems. Subsequently, for plant models with parametric-type uncertainty, new vertex results related to robustness margins and system performance are derived. Based on this, new tools to design robust low-order controllers for such systems are presented.

In this paper, we address the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a directed graph. A distributed adaptive control algorithm with an adaptive gain design using both relative position and velocity feedback is proposed based on the approximation capability of neural networks. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, we show a necessary and sufficient condition on leaderless consensus for networked Lagrangian systems under a directed graph with unknown nonlinearities and external disturbances, in which the systems achieve consensus asymptotically. We then propose a distributed containment control algorithm without using neighbors' velocity information.